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Jade was working on her statistics homework. One of the questions gave her a trend line and asked her to find the residuals. Sh...Question
Jade was working on her statistics homework. One of the questions gave her a trend line and asked her to find the residuals. She found the following residuals 2.6, 9.3, −5.489
, and −6.59
. What conclusion can Jade make about the linear model based on the residuals?
The linear model seems to accurately represent the data since the residual 2.6 means that the actual point is not far from the estimate.
The linear model seems to accurately represent the data since the residual 2.6 means that the actual point is not far from the estimate.
The linear model does not accurately represent the data since half of the residuals are positive and half of the residuals are negative.
The linear model does not accurately represent the data since half of the residuals are positive and half of the residuals are negative.
The linear model does not accurately represent the data since the residual 9.3 means that the actual point is far from the estimate.
The linear model does not accurately represent the data since the residual 9.3 means that the actual point is far from the estimate.
The linear model seems to accurately represent the data since half of the residuals are positive and half of the residuals are negative.
The linear model seems to accurately represent the data since half of the residuals are positive and half of the residuals are negative.
, and −6.59
. What conclusion can Jade make about the linear model based on the residuals?
The linear model seems to accurately represent the data since the residual 2.6 means that the actual point is not far from the estimate.
The linear model seems to accurately represent the data since the residual 2.6 means that the actual point is not far from the estimate.
The linear model does not accurately represent the data since half of the residuals are positive and half of the residuals are negative.
The linear model does not accurately represent the data since half of the residuals are positive and half of the residuals are negative.
The linear model does not accurately represent the data since the residual 9.3 means that the actual point is far from the estimate.
The linear model does not accurately represent the data since the residual 9.3 means that the actual point is far from the estimate.
The linear model seems to accurately represent the data since half of the residuals are positive and half of the residuals are negative.
The linear model seems to accurately represent the data since half of the residuals are positive and half of the residuals are negative.
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Answered by
GPT-4o mini
In evaluating the residuals provided by Jade (2.6, 9.3, -5.489, and -6.59), she can draw conclusions based on the values of these residuals. Here's how to interpret them:
1. Positive residuals (like 2.6) indicate that the actual data point is above the predicted value, while negative residuals (such as -5.489 and -6.59) indicate that the actual point is below the predicted value.
2. The presence of both positive and negative residuals suggests that the model has some systematic deviations — in other words, the line doesn't fit perfectly through the data.
Among the residuals, the residual of 9.3 is particularly noteworthy, as it indicates a substantial difference between the predicted and actual value, suggesting that the linear model may not capture the data accurately.
Given these points, the most accurate conclusion for Jade to make about the linear model based on the residuals is:
**The linear model does not accurately represent the data since the residual 9.3 means that the actual point is far from the estimate.**
This statement directly addresses the significant positive residual and highlights the inadequacy of the model, as it indicates that there are values that diverge considerably from the predictions of the linear trend line.
1. Positive residuals (like 2.6) indicate that the actual data point is above the predicted value, while negative residuals (such as -5.489 and -6.59) indicate that the actual point is below the predicted value.
2. The presence of both positive and negative residuals suggests that the model has some systematic deviations — in other words, the line doesn't fit perfectly through the data.
Among the residuals, the residual of 9.3 is particularly noteworthy, as it indicates a substantial difference between the predicted and actual value, suggesting that the linear model may not capture the data accurately.
Given these points, the most accurate conclusion for Jade to make about the linear model based on the residuals is:
**The linear model does not accurately represent the data since the residual 9.3 means that the actual point is far from the estimate.**
This statement directly addresses the significant positive residual and highlights the inadequacy of the model, as it indicates that there are values that diverge considerably from the predictions of the linear trend line.
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